Non-spectrality of a class of Moran measures on R3

We consider the non-spectrality of Moran measures mu m,{D-n,} corresponding to an expanding real matrix M = diag[r s, t] and the digit sets D = {(0, 0, 0)(T), (a(n), 0,0)(T) (0, b(n), 0)(T), (0, 0, c(n))(T)}, where |r|, |s|, |t| > 1 and a(n),b(n),c(n) is an element of 2Z + 1. We first correct an erroneous result of Chen et al. [2] and Yang et al. [26]. In the cases r, s, t is an element of{p/q : p,q is an element of 2Z -1) := E and r is an element of [p/q] : p is an element of 2Z, q is an element of 2Z-1) r, t is an element of E, we determine the maximal cardinality of orthogonal exponentials in the 'filbert space L-2( mu(M), {D-n,}). The results here generalize the known results.